I841.J 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



427 



distance are measured by 33'3 feet, ami of course under four or five chains 

 distance, the rending staff or ordinary dimensions will be very convenient ; 

 but with the 20 inch level erecting telescope, 1000 links in dist'irice are read 

 off by 13'S feet, therefore a 11 feet staff is very convenient for this telescope 

 for all distances under 10 chains, and by having a longer staff, or liy taking 

 a semi-diameter or other known proportion of the diapliragm, tlie lengtli of 

 the observed distance may be increased at pleasure, and be limited only by 

 the i)ower of tlie telescope to read the staff distinctly. Taking facility of 

 reading the staff and tlie consequent accuracyof the observations for ordinary 

 levelling operations into account, distances not e?;cccdtng from 3 to 5 chains 

 for the small 10 inch level, and from 7 to 12 chains for the large 20 inch 

 level described above, are the best and most convenient, as insuring speed 

 with most accuracy; but any distance, down to 12 feet by the small level 

 and 20 feet by the large level, can l)e found quite accurately ; at distances 

 smaller'than these, the range of the sliding tube is too short to admit of dis- 

 tinct vision, but it is not important to have this range increased, as distances 

 smaller than these are not often required, and when so, the levelling i-od fur- 

 nishes the ready means of ascertaining the amount by direct application. 



The large telescope, with the erecting eye-piece, is decidedly superior for 

 the purpose of measuring distances to the smaller one ; but care must be 

 t,iken that the diaphragm of the object-g'ass is not at all intercepted l)y the 

 diaphragm of the eye-piece, which is nearer to the eye, and this can easily be 

 found out by illuminating the diaphragm of the eye-piece by a piece of white 

 paper, and then liy giving the eye-tube a motion in its slide to or from the 

 diaphragm of the object-glass. By this means the two diapliragins will be- 

 come apparent, and if, wlien the eye-tube is fixed at the proper adjustment 

 for viewing the cross-lines, the diaphragm in the eye-tube intersects in flie 

 smallest degree (for these circles are not always concentric) that of the ob- 

 ject-glass, or with t!ie cross lines, then the diameter of this latter must be 

 contracted by points or screws projecting at equal distances into the field of 

 ^^ew, so far as to clear the inner circumference of lire diaphragm of the eye- 

 piece, and these screws, vrhen driven to their proper places, must he so firmly 

 fixed that they will not readily be disturbed. No doubt the fine lines of a 

 spider's web, or very fine wire, might answer the same purpose ; but as the 

 eye-tube in the generality of good telescopes of this sort has to be taken out 

 and replaced on every occasion of its use, it is difficult to divest the mind of 

 the possibility of tlie lines being disturbed Ijy this motion, whereas in the 

 case of tlie inflexible metal of the diaphragm no such objection can possibly 

 hold good ; moreover, the cross lines serve as a guide to find the true diame- 

 ter. 0))ticians have been in the habit of placing tivo parallel upright lines, 

 and at right angles to these a horizontal line, in the field of view of the tele- 

 scope, and some people have the idea that these may be used for the purpose 

 of distances, but besides the objection stated above they have two very serious 

 objections — the first is that they should have been horizontal for this purpose, 

 and the second is that they are much too close together and incluiJe much 

 too small an angle to give more than an approximation to the distance, and 

 it may he added, that they never were intended for anything of (he kind, but 

 probably only as a guide to keep the reading start' vertical while taking levels, 

 but in the case of extraordinarily long distances these cross lines may be ser- 

 viceable in taking semi-diameters, &c. 



The constant quantity for the lO-incii level being "07, and for the 20-inch 

 level '05, and as these telescopes or levels are nearly of the smallest and 

 largest sizes used for general purposes, the constant in feet for a medium size 

 may be somewhere at about "00 feet. 



In favour of this method of observing distances it may be mentioned that 

 ■with the telescope of the 20-inch level, and witli no further adjustment for 

 focal distance of the object-glass than what appeared at each observation to 

 be distinct vision, distances can be taken of many miles by the accumuiation 

 of distances such as those required in levelling; that is to say, not often less 

 than 20 feet, often averaging 8 chains, and seldom so much as 20 chains, 

 with quite as much accuracy as Ijy the common method of the chain. The 

 superior accuracy of the measurements taken from the reading staft' during 

 the process of levelling a circuit of many miles and returning to the same 

 point, when, on balancing the numerous rises and falls, the near agreement 

 within an inch or so proves the accuracy of the work, also favours the idea 

 that this method of measuring distances is capable of great accuracy, for the 

 self-same staft" is used, and the vertical position is the most natural and least 

 difficult to find, and the level itself gives the telescope the horizontal direc- 

 tion. From all tliese causes, and from the perpetual inequality of the ground 

 in chaining, there can be no doubt that, on these heads at least, this method 

 has superior claims to the chain in point of precision, and as a further refine- 

 ment, will hs especially of great service to those telescopes whose defining 

 ]iower is not of the first-rate description, and, for any telescope, removes all 

 doubts of want of precision. 



Let the aberrations for focal length for every distance of the object be 

 graduated upon the slide of the large tube, from the principal focal mark be- 

 fore mentioned to the extremity of the slide. The aberration or distance 

 from this principal focal mark is found thus. 



length of the focus for near objects ought to he obtained by having the lack 

 and slide adjustment beliind the centre, and not in front ; from this it appears 

 that those tubes which move at the object-glass, are not precisely adapted 

 for this method, inasmuch as the increased distance of the object-glass from 

 the centre of the station would, for the short distances, increase the length 

 of -Yr/, and of course the constant would have to undergo a similar increase, 

 •.vhicli would be absurd. 



Without referring to (he former figures, the principal focal distance is gene- 

 rally called F, and the distance of the object from the object-glass is called 

 simply D, and these two being given, the aberration which is called e is found 

 by the formula in optics, which is this : — ■ 



F- 



From this formula, a table of aberrations can be calculated for as many 

 distances as the short slide of the tube is capable of receiving, and of having 

 graduated upon it ; but what would be better still, instead of or in addition 

 to the scale for actual distances, would be to have a scale of readii>gs of the 

 staff; or in other words, the adjustment for focus should correspond with the 

 reading of the staff. 



Now, it has been shown that the reading of the staft" varies as J)— Fvaries; 

 but D—f^ y. e = F'-; now F- is a constant quantity, and D—F^is a variable 

 quantity, therefore e is also variable, and as the product of these two variables 

 is always a constant quantity, it follows that e varies iaverscly, as D — F^ 

 therefore also e varies inversely as the reading of the staff; that is to say, 

 when the rays are parallel and the distance infinite, and consequently the 

 reading infinite, tlien the aberration is Zero, or at the principal focal mark ; 

 again, when the reading is at Zero and D—F = 0, or D = F, or when the staff 

 is held at the principal anterior focus, then the aberration is infinite ; again, 

 taking the case when Z) — F=F, Iheue — F; for D — F a e = F-, tind also 

 Z)=2 F; that is to say, when the distance is twice the ))rincipal focal dis- 

 tance from the object-glass, the aberration e and focal distance i^are equal. 



Now, because the aberration varies inversely as the distance D — F. 



Whenfl-F=0, 

 When D-F=F, 

 WhenD-jF'=2F', 



Wheni)-F=4F, 



&c. 

 ■F, will be proportional to Zero, 



When J5-F=100F, 



When D — F— infinity, 

 &c. &c. 

 Now, the readings, always varying as D 



F F 



F, 2F, iF, &c., and the aberrations for these readings to infinity, F, ' — ' 



&c. This furnishes a very ready method for graduating the sliding tube of 

 the telescope with the aberrations for the dift"erent readings which must be 

 marked thereon in figures. 



Taking a practical example, the large telescope of the level (181- inches 

 principal focal length) when the slide is out 1'6 inches beyond the princijial 

 focus, or nearly its extreme length, making the augmented focal length 20'1 

 inches; then when the reading is properly taken for this adjustment, that is 

 to say, the staft' held at the requisite distance for distinct vision, the reading 

 is found to be •10 feet. 



Then, since the reading varies inversely as the distance, the follow ing shows 

 how a table of aberrations for any reading may be constructed, thus — 

 When the reading The aberration at The aberration from 



is -40 into the inverse principal focal point 



ration of the reading 



•40 feet 1-GOx ^ 



■50 do I'OO X 



•60 do l'60x 



•80 do 1-GOx fS . 



1-00 do 1^00 X -5^. 



1-60 do 1-60 X -^. 



4-00 do l^GOx ,^ . 



8-00 do V60x ^. 



lG-00 do l-GOx-j^ii^. 



32-00 do 1-60 X54^. 



&o. 

 Now, the reading of 32 feet corresponds with a distance of 23 chains ; so 

 then at a distanct of little more than a quarter of a mile the aberration is 

 only the -^ part of an inch, and at 46 chains the -iff part of an inch. Be- 

 yond this distance, therefore, the principal focal mark will l-e quite near 

 enough without any further subdivisions ; for, although they can bo carried 

 to any wished for degree of minuteness, yet supposing that the ailjustnicut 

 for focal distance was not nearer than the -^Irn P^'' of ^" ''i'^''' *''^ ^''^^ °^ 

 the image being exactly in proportion to the focal distance, and this distance 

 being supposed to be in error by the -^ part of an inch, then the -^ part 

 of an inch over a space of 18-5 inches is only the ttStt P^''' of "'^ whole, 

 and when the focal distance is 20 inches, the -j-^ part of an inch will be the 

 ■iriyTjx; part ofthe whole, and thus the reading, and consequently the distance, 

 true to the .^ „'„ „ part of the whole. 



For the sake of rendering the demonstration more simple, the scale above 



3 L 2 



4S gives 



